Pendulum Problem: Potential energy equals? kinetic energy

  1. 1. The problem statement, all variables and given/known data

    A pendulum consists of an object of mass m = 1.65 kg swinging on a massless string of length l. The object has a speed of 1.97 m/s when it passes through its lowest point. If the speed of the object is 0.87 m/s when the string is at 70° below the horizontal, what is the length of the string?

    Correct answer: 2.64 m (to 3 sig figs)

    2. Relevant equations

    Ep = mgh
    Ek = 1/2mv^2

    3. The attempt at a solution

    I tried the equation:

    mg(length(1-cos20°)) = 1/2mv^2

    and this did not work.. it worked when I had the length and needed the velocity?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. PeterO

    PeterO 2,319
    Homework Helper

    Using your two speeds, you can calculate the kinetic energy at the bottom, and when in the 70 degree position [or indeed 20 degree as you are starting to use]
    The reduction in kinetic energy will be accompanied by an equivalent increase in Potential energy - so you know the gain in height.

    A bit of trig on the triangle formed should yield the pendulum length you are after.
  4. Thank you so much!
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